Global study of functional equations and special functions

1.对于I、II、IV型的Painleve超越，我们估计了其增长阶数。结果如下：对于I，P_I=5/2;<II>对于II，P_3 = 3/2;对于IV<IV>，P_4 = 2. 2.证明了所有Painleve方程的Painleve性质. 3.研究了泛覆盖空间上第三类和第五类Painleve方程的解，得到了增长阶的估计. 4.得到了第一类Painleve方程族解的增长阶的一个较低估计，5.给出了一系列与第一Painleve族等价的微分方程组，并证明了Painleve性质。6.估计了具有双周期系数的Riccati方程解的增长级。

1.For Painleve transcendents of I, II, IV types, we estimated the growth order. The results are as follows : P_I=5/2 for I ; 3/2【less than or equal】P_<II>【less than or equal】3 for II ; and 2【less than or equal】P_<IV>【less than or equal】4 for IV.2.We proved the Painleve property for all Painleve equations.3.We considered solutions of the third and the fifth Painleve equations on the universal covering space, and obtained some estimates for the growth order.4.We obtained a lower estimate for the growth order of solutions of the first Painleve hierarchy, and also estimated the frequency of poles and α-points of them.5.We presented a series of systems of differential equations which is equivalent to the first Painleve hierarchy, and proved the Painleve property.6.We estimated the growth order of solutions of Riccati equations with doubly periodic coefficients.